A tourist stops to read a sign posted outside the Library of Congress in Washington on Sunday, notifying visitors that all LOC buildings will be closed to the public in the event of a temporary government shutdown. (Bill Clark/CQ Roll Call)

If a bipartisan group of some 20 senators trying to negotiate a deal on immigration to end the government shutdown are looking for a commitment from House Republicans, they’re unlikely to get one.

Rank-and-file GOP members said the House will not be bound by any agreement reached across the Capitol on immigration, something Senate Democrats say is key to ending their filibuster of a three-week stopgap bill the chamber is planning to vote on around 1 a.m. Monday.

“I don’t see any of our people interested in some half-baked idea that’s produced by a self-appointed group of senators,” Oklahoma Rep. Tom Cole said. “The only thing the speaker tells us that he has signaled to [Senate Majority Leader Mitch] McConnell he can do is change the dates.”

Speaker Paul D. Ryan said Sunday on CBS’s “Face the Nation” that the shutdown “blew up” bipartisan, bicameral negotiations that were underway on an immigration measure to include border security and a replacement for the Deferred Action for Childhood Arrivals, or DACA, program .

A bipartisan proposal from Sens. Lindsey Graham of South Carolina and Richard J. Durbin of Illinois is one that House Republicans and President Donald Trump don’t support, Ryan said.

“It was an end run around of the negotiations we had,” the Wisconsin Republican said, referring to talks that had been occurring between the No. 2 congressional leaders, which included Durbin, the Senate minority whip.

The House Republican Conference huddled briefly Sunday, but members came out saying nothing had changed from their perspective. They were still waiting on the Senate to pass a continuing resolution that would reopen the government before resuming any negotiations on immigration.

“Republicans are still very united,” said Republican Study Committee Chairman Mark Walker of North Carolina. “It’s amazing. It’s one of the few times in the three plus years I’ve been here, it’s legitimate. I mean, the guys are together.”

While House GOP leaders had little to update their members on Sunday, the conference meeting was an alternative to holding a quorum call to make sure lawmakers had heeded their notice to stay in town, Freedom Caucus Chairman Mark Meadows told reporters.

“Having a short conference meeting is also an indication that there is not a whole lot that the House can do,” the North Carolina Republican said. “We’ve got to wait for a Democrat senator to make up his mind on what he wants to do with regards to opening the government back up.”

Meadows was referring to Senate Minority Leader Charles E. Schumer, whom Republicans have blamed for the shutdown. On Sunday, Schumer’s deputy, Durbin, appeared to be leading negotiations on behalf of Democrats with the bipartisan group of senators trying to reach a deal on immigration.

Watch: DACA Protesters Sit on Senate Steps, Get Arrested

House guarantee needed?

Durbin told reporters the group was looking for a guarantee that an immigration bill similar to one he and Graham have proposed would get a vote on the Senate floor. Some Senate Democrats have also suggested they’d like some kind of commitment for a House vote as well.

House Minority Leader Nancy Pelosi told reporters Sunday her caucus would be looking for assurances for a Senate and House vote on a bipartisan immigration deal. She also said House Democrats would not support another CR without a deal to increase the sequestration spending caps, with “parity” (equal increases in defense and nondefense spending) and “pay-fors.”

But if the House does take up an immigration bill, it’s not going to be the Graham-Durbin proposal, Cole said, suggesting senators are repeating the mistakes of the 2013 immigration negotiations. That effort, also led in part by Graham and Durbin, resulted in a bipartisan measure that passed the Senate but had little support in the House, where it was never brought up.

“Lindsey Graham and [Arizona Sen.] Jeff Flake don’t represent where the majority of Republicans in the Senate are, let alone here, so how can they be the lead negotiators on that?” Cole said. “I just don’t think that’s likely.”

But Rep. Charlie Dent, co-chairman of the moderate Tuesday Group, said Congress is “in a much different place” than 2013 when immigration talks collapsed.

“We have a deadline, March 5,” the Pennsylvania Republican said. “And there’s a lot of pressure to do this.”

Dent said Ryan would be under “tremendous pressure” to bring up a bipartisan bill passed by the Senate, regardless of whether the majority of House Republicans opposed it, something the congressman said was likely.

“If the Senate is able to secure over 60 votes for a DACA security bill, I can’t imagine that same bill would receive a majority of House Republicans,” he said.

Ryan, however, has said he believes he can get a majority of his conference to support a bipartisan DACA solution, mainly because Trump has to sign whatever compromise measure is reached. Indeed, conservatives believe that Trump’s interests are aligned with their own.

“If he negotiates a deal, whether it’s directly with Sen. Schumer or a group of individuals, I think he will stand fast with the principles that he’s long espoused,” Meadows said of Trump. He was referring to the president’s requests for funding construction of a wall along the southern border and ending extended family-based visas and the visa lottery program.

‘Queen of the Hill’

Dent, who doubts such a conservative measure could pass the House, suggested the chamber just adopt a strategy known as “Queen of the Hill.” The process involves putting several bills on the floor and accepting the one that gets the most votes.

In addition to the Graham-Durbin proposal, Dent suggested the House could vote on a more hard-line measure by House Judiciary Chairman Robert W. Goodlatte and a bipartisan bill by Texas GOP Rep. Will Hurd and California Democratic Rep. Pete Aguilar.

“I bet that either Hurd or Graham-Durbin would get the most votes, one of those two,” he said.

Dent’s suggestion for the House is effectively where Senate negotiations are headed. But that still won’t produce a measure that the House will be bound to pass.

“As we are frequently reminded, it is a bicameral system,” Florida GOP Rep. Matt Gaetz said.

Senate negotiations that don’t include House leaders and the White House aren’t particularly promising, Cole said.

“Just because they accept something, doesn’t mean we will, certainly doesn’t mean the the administration will,” the Oklahoma Republican said. “It seems to me like there’s a lot of scrambling around over there but there’s not much of a clear plan.”

While senators were scrambling, some House Republicans were planning to watch football and eat food in the majority whip’s office after the conference meeting. Others saw food as one of the reasons for attending the GOP conference meeting given that there were no new updates for leadership to report.

“I think that the speaker kind of — he over-includes and over-communicates with the membership even when there’s not a big update,” Gaetz said. “Some people were hungry. We had sandwiches.”